Model Building and Anisotropy of PrFeB Permanent Magnetic Materials

This paper considers that the crystal grains of HDDR Pr2Fe14B permanent magnetic material are cubic, the size is 0.3 μm, and the crystal grains are in simple cubic accumulation. It is considered that there are boundary phases between grains. It is assumed that the boundary phases are non-magnetic phases with the thickness of d, and evenly distributed between grains. The anisotropy expression of single grain boundary is given considering structure defect and intergranular exchange coupling interaction. Based on micro-magnetic simulation calculation, the variation of the average anisotropy of a single grain with the structural defects and boundary phases was calculated. The results show that when the thickness of structural defects is constant, the average anisotropy of a single grain decreases with increasing of grain boundary phase thickness, and while the thickness of grain boundary phase is constant, it also decreases with increasing of structural defect thickness.


Introduction
HDDR (Hydrogenation, Disproportionation, Desorption, Recombination) process is now well established as an effective process for preparing anisotropic NdFeB magnetic powders [1] [2] [3]. Theoretically, the structure, lattice constant, magnetocrystalline anisotropy constant, exchange integral constant and saturation magnetization of Pr 2 Fe 14 B and Nd 2 Fe 14 B are very close [4]. Since the intrinsic magnetic properties of Pr 2 Fe 14 B-type alloy are comparable to those of Nd 2 Fe 14 B-type alloy, recently researchers had attempted the HDDR process to DOI: 10 [9] investigation shows that as long as disproportionation time is reasonably controlled, the disproportionation products display a rod-like microstructure with self-organized hexagonal PrH 2 nanorods embedded in Fe matrix, and the highly ordered rod-like structure is responsible for the high degree of texture orientation of HDDR Pr 13 Fe 79.4 B 7 Nb 0.3 Ga 0.3 magnetic powders. Zhong [10] adopted the modified HDDR process to prepare pure ternary anisotropy Pr 2 Fe 14 B-type magnetic powders. At present, there is much experimental research work on PrFeB permanent magnetic materials, and no theoretical research work has been seen. This paper attempted to establish the anisotropy theoretical model of PrFeB permanent magnet material, and further investigated the anisotropy variation of magnetic powders with structural defects and grain boundary phase. It hopes that these results of this paper can provide theoretical guidance for the experimental preparation of highly anisotropic magnetic powders.

Theory Model of Pr2Fe14B-Type Magnetic Powders
Assumed that the HDDR Pr 2 Fe 14 B grain is a cube with size of 0.3 μm, and these grains are stacked in simple cubic form, as shown in Figure 1. represents a single grain, represents the boundary phase. The grain is affected by the exchange coupling interaction between adjacent grains. For a single crystal grain, due to its face center, the rib and the apex angle own to different contact conditions with adjacent grain, therefore, the anisotropy of three regions is also different. The plane-centered region of grains is only affected by the exchange coupling of adjacent single grains, denoted as N = 1. The edge regions are affected by adjacent three grains, denoted by N = 3. The top Angle regions are affected by adjacent seven grains, denoted by N = 7.
Arcas [11] considered that a single crystal of a nano-magnet is directly connected to the surrounding N-grain, and used this expression K 1 (r) = K 1 /N 1/2 to describe anisotropy variation of grain surface. Based on the special microstructure of HDDR Nd 2 Fe 14 B grains, the grain surface is affected by both exchange coupling interaction and structural defects. When the grain surface structure defect thickness r 0 is less than the exchange coupling interaction length lex/2, Liu indicate the surface anisotropy change of Nd 2 Fe 14 B grain. When the surface structure defect thickness r 0 of the grain is larger than the exchange coupling interaction length lex/2, Liu [12] used this expression ( ) to represent the surface anisotropy change of Nd 2 Fe 14 B grain.
Not only the intrinsic magnetic properties of Pr 2 Fe 14 B-type alloy are comparable to those of Nd 2 Fe 14 B-type alloy, but also the microstructure of the Pr 2 Fe 14 B magnetic powder grains is similar to that of the Nd 2 Fe 14 B magnetic powder grains [9], thus, this paper considered that the change of surface anisotropy of Pr 2 Fe 14 B grains is similar to that of surface anisotropy of Nd 2 Fe 14 B grains. Since the grains of the Pr 2 Fe 14 B magnetic powder are stacked in a simple cubic structure, The face of a single grain directly contacts with one grain (record as N = 1), the ridge of a single grain directly contacts with three grains (record as N = 3), and corner regions of a single grain directly contact with seven grains (record as N = 7), the anisotropy change of the three regions is related to N, thus, the surface anisotropy K(r) of Pr 2 Fe 14 B grain can be rewritten as: When the structure defect thickness r 0 of grain surface is smaller than the exchange coupling interaction length lex/2 ( ) ( ) When the structure defect thickness r 0 of grain surface is larger than the exchange coupling interaction length lex/2 where K 1 is the normal magnetocrystalline anisotropy constant, r 0 is the structure defect thickness of grain surface, r is the distance to the grain intergranular center, lex is the exchange coupling length between grains, d is the boundary phase thickness.

Anisotropy of Pr2Fe14B Grain
Boundary defect zone anisotropy of Pr 2 Fe 14 B grain 1 K ′ can be expressed as: The average anisotropy K of a single grain can be expressed as: where,   , But in 1.85 4 r < < , the anisotropy is only affected by structural defects. Figure 8 shows the variation of material average anisotropy K with structure defect thickness d. This figure indicates that for r 0 taking different values, K decrease with increasing of d.

Conclusion
This paper investigates the effects of exchange coupling interactions and structural defects on the anisotropy of a single grain. The results show that both structure defects and exchange coupling interactions affect the anisotropy of single grains. When the thickness of structural defects is constant, the average anisotropy of a single grain decreases with increasing of grain boundary phase thickness, and while the thickness of grain boundary phase is constant, it also decreases with increasing of structure defect thickness.